In this paper, we introduce the notion of set of epsilon-proper equilibria for a bimatrix game. We define a 0-1 mixed quadratic program to generate a sequence of epsilon-proper Nash equilibria and show that the optimization results provide reliable indications on strategy profiles that could be used to generate proper equilibria analytically. This approach can be generalized in order to find at least one proper equilibrium for any bimatrix game. Finally, we define another 0-1 mixed quadratic program to identify non-proper extreme Nash equilibria. Crown Copyright (C) 2011 Published by Elsevier Ltd. All rights reserved.